What is a particle-conserving Topological Superfluid?

TL;DR

This paper proposes a new criterion based on many-body fermionic parity switches to identify topological superfluidity in particle-number conserving fermionic systems, linking it to observable phenomena like the fractional Josephson effect.

Contribution

It introduces a novel, parity-based criterion for topological phases in interacting fermionic systems and demonstrates its application to the Richardson-Gaudin-Kitaev chain, including the construction of many-body Majorana modes.

Findings

The criterion successfully distinguishes topologically trivial and non-trivial superfluids.

Application to the Richardson-Gaudin-Kitaev chain confirms the criterion's effectiveness.

Constructed many-body Majorana modes in a particle-number conserving framework.

Abstract

We establish a criterion for characterizing superfluidity in interacting, particle-number conserving systems of fermions as topologically trivial or non-trivial. Because our criterion is based on the concept of many-body fermionic parity switches, it is directly associated to the observation of the fractional Josephson effect and indicates the emergence of zero-energy modes that anticommute with fermionic parity. We tested these ideas on the Richardson-Gaudin-Kitaev chain, a particle-number conserving system that is solvable by way of the algebraic Bethe ansatz, and reduces to a long-range Kitaev chain in the mean-field approximation. Guided by its closed-form solution, we introduce a procedure for constructing many-body Majorana zero-energy modes of gapped topological superfluids in terms of coherent superpositions of states with different number of fermions. We discuss their significance and the physical conditions required to enable quantum control in the light of superselection rules.